Finite Group Databasebeta

← #14807413

Subgroups — #14807413

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622687C211yesmaximal, characteristic, complemented
2C2×#10622681C211yesmaximal, characteristic, complemented
3#13074373C211yesmaximal, characteristic, complemented
4#13069619C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069586C211yesmaximal, characteristic, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068950C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic, complemented
11C2×C11×#540C211yesmaximal, characteristic, complemented
12C11×#540—24no—
13C11×#540—24no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×#121—22no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2212yes—
20C2×C11×#117C2211yescharacteristic
21C22×#4324C2212yes—
22C22×#4323C2212yes—
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66928C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622687—24no—
30#10622681—24no—
31#10622607—22no—
32C2×#66874C2212yes—
33C2×#66873C2212yes—
34#10622574—22no—
35#10622552C2211yescharacteristic
36#10622548C2211yescharacteristic
37#10622542C2211yescharacteristic
38C2×#66867C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11C2312yes—
46C23×C4×C11—22no—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C22×D44C2311yescharacteristic
50C22×Dic22C2311yescharacteristic
51C11×#127—22no—
52C11×#127D414yescomplemented
53C11×#125—22no—
54C11×#125D414yescomplemented
55C11×#123—216no—
56C11×#121—216no—
57C11×#121—24no—
58C11×#121—24no—
59C4×D4×C11—24no—
60C4×D4×C11—24no—
61C11×#117—22no—
62C11×#117—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—21no—
72C2×#4324—24no—
73C2×#4324—24no—
74C2×#4324—42no—
75C2×#4323—24no—
76C2×#4323—24no—
77C2×#4323—42no—
78#66983—42no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85#66977—42no—
86C2×Dic11⋊C4—21no—
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2312yes—
89#66928—22no—
90#66928—22no—
91#66896—42no—
92#66896—42no—
93C11⋊#95—22no—
94C22⋊(C11⋊C8)—24no—
95#66874—24no—
96#66873—24no—
97#66867—22no—
98C4×C11⋊C8—22no—
99#25611—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11C2×D411yescharacteristic
102C23×D11—21no—
103C2×D4×C11—28no—
104C2×D4×C11—28no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—82no—
111C2×D4×C11—82no—
112C2×D4×C11—82no—
113C2×D4×C11—82no—
114C2×D4×C11C2×D414yes—
115C22×C4×C11—22no—
116C22×C4×C11—28no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—82no—
122C22×C4×C11—82no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—42no—
128C2×C22⋊D11—82no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—22no—
135C2×D44—22no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4C2×D414yes—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—24no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11C2×D412yes—
150C42×C11C2×D412yes—
151C22⋊Dic11—42no—
152#4324—48no—
153#4323—48no—
154(C2×D11)⋊C4—42no—
155(C2×D11)⋊C4—44no—
156(C2×D11)⋊C4—82no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—82no—
160Dic11⋊C4—42no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8#4114yes—
167C2×#540D1111yescharacteristic, complemented
168C2×#496—111no—
169C2×#488—111no—
170#2620—111no—
171#2000—112no—
172#1999—112no—
173#1992—111no—
174#1957—111no—
175#1879—112no—
176#1877—112no—
177#1750—111no—
178C23×C11—21no—
179C23×C11—24no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—42no—
195C22×D11—42no—
196D4×C11—24no—
197D4×C11—24no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—88no—
201D4×C11—88no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—88no—
216C2×C4×C11#12014yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4112yes—
220C2×C4×C11H(5,𝔽2)12yes—
221C22⋊D11—84no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229D44—42no—
230D44—42no—
231Dic22—42no—
232Dic22—42no—
233C11⋊C8—24no—
234C11⋊C8—42no—
235C22×SD16—112no—
236C22×D8—112no—
237#540—24no—
238#540—24no—
239C2×#127C2×D1111yescharacteristic
240C2×#125C2×D1111yescharacteristic
241C2×#124—111no—
242C2×#123—22no—
243C2×C22⋊Q8—111no—
244C2×#121—22no—
245C2×#121—111no—
246C2×#121C2×D1112yes—
247C2×C4×D4C2×D1112yes—
248C2×#117C2×D1111yescharacteristic
249#496—224no—
250#488—224no—
251C2×#103—112no—
252C2×#102—112no—
253C2×#102—112no—
254C2×#102—112no—
255C2×C22⋊C8—112no—
256C2×#97—111no—
257C2×C4×C8—111no—
258#396—222no—
259#394—222no—
260#391—111no—
261#390—111no—
262#384—111no—
263#340—112no—
264#340—112no—
265#336—112no—
266C22×C11—42no—
267C22×C11—41no—
268C22×C11—44no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—44no—
272C22×C11—42no—
273C22×C11—44no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11C2×#12011yescharacteristic
279C22×C11#53211yescharacteristic
280C22×C11#53511yescharacteristic
281C22×C11#57612yes—
282C22×C11#57712yes—
283C2×D11—82no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—82no—
288C4×C11—24no—
289C4×C11—41no—
290C4×C11—42no—
291C4×C11—44no—
292C4×C11#54612yes—
293C4×C11#55012yes—
294Dic11—81no—
295Dic11—81no—
296Dic11—81no—
297C22×Q8—111no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—111no—
301C22×D4—221no—
302C22×D4C22×D1112yes—
303C23×C4—22no—
304C23×C4C22×D1111yescharacteristic
305C2×SD16—224no—
306C2×SD16—224no—
307C2×SD16—442no—
308C2×D8—224no—
309C2×D8—224no—
310C2×D8—442no—
311C22×C8—112no—
312C22×C8—112no—
313#127—22no—
314#127C22⋊D1114yescomplemented
315#125—22no—
316#125C22⋊D1114yescomplemented
317#124—222no—
318#124—222no—
319#123—216no—
320C22⋊Q8—442no—
321#121—216no—
322#121—24no—
323#121—24no—
324#121—442no—
325C4×D4—24no—
326C4×D4—24no—
327#117—22no—
328#117—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4C22⋊D1112yes—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—221no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4C22⋊D1112yes—
343C2×C42C22×D1111yescharacteristic
344C2×C42C22×D1111yescharacteristic
345#103—224no—
346#102—224no—
347#102—442no—
348#102—442no—
349C22⋊C8—224no—
350#97—222no—
351C4×C8—222no—
352#95—222no—
353C2×C11—81no—
354C2×C11—84no—
355C2×C11#243111yescharacteristic
356C2×C11#301212yes—
357C2×C11#317912yes—
358C2×C11#322011yescharacteristic
359C2×C11#322111yescharacteristic
360D11—161no—
361C24—22no—
362C24—221no—
363C24C2×C22⋊D1111yescharacteristic
364C2×Q8—222no—
365C2×Q8—222no—
366C2×Q8—221no—
367C2×Q8—221no—
368C2×D4—28no—
369C2×D4—28no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—82no—
376C2×D4—82no—
377C2×D4—82no—
378C2×D4—82no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—221no—
382C2×D4—221no—
383C2×D4—442no—
384C2×D4—882no—
385C2×D4C2×C22⋊D1114yes—
386C22×C4—22no—
387C22×C4—28no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—82no—
393C22×C4—82no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—221no—
397C22×C4C2×C22⋊D1112yes—
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1112yes—
400C22×C4C23×D1111yescharacteristic
401SD16—448no—
402D8—448no—
403C2×C8—114no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—222no—
408C2×C8—222no—
409C4⋊C4—28no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—442no—
415C4⋊C4—882no—
416C4⋊C4C2×C22⋊D1114yes—
417C22⋊C4—28no—
418C22⋊C4—28no—
419C22⋊C4—24no—
420C22⋊C4—442no—
421C22⋊C4—442no—
422C22⋊C4—444no—
423C22⋊C4—882no—
424C42—21no—
425C42—21no—
426C42C2×C22⋊D1112yes—
427C42C2×C22⋊D1112yes—
428C11#2561111yescharacteristic, complemented, Sylow
429C23—21no—
430C23—21no—
431C23—22no—
432C23—22no—
433C23—21no—
434C23—24no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—441no—
442C23—441no—
443C23—442no—
444C23—442no—
445C23—441no—
446C23C22×C22⋊D1111yescharacteristic
447Q8—442no—
448Q8—442no—
449D4—24no—
450D4—24no—
451D4—42no—
452D4—42no—
453D4—88no—
454D4—88no—
455D4—442no—
456D4—442no—
457D4—884no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—24no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—88no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—441no—
479C2×C4#6700614yes—
480C2×C4#41×D1112yes—
481C2×C4#6704212yes—
482C2×C4C22×C22⋊D1111yescharacteristic
483C2×C4C22×C22⋊D1111yescharacteristic
484C8—224no—
485C8—442no—
486C22—42no—
487C22—41no—
488C22—44no—
489C22—41no—
490C22—41no—
491C22—44no—
492C22—42no—
493C22—44no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—882no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—882no—
503C22#1062336111yescharacteristic
504C22#1062336311yescharacteristic
505C22#1062336612yes—
506C22#1062336712yes—
507C22C2×#6700611yescharacteristic
508C4—24no—
509C4—41no—
510C4—42no—
511C4—44no—
512C4—881no—
513C4—881no—
514C4—881no—
515C4#1062336012yes—
516C4#1062336512yes—
517C2—81no—
518C2—84no—
519C2—1761no—
520C2#1307223111yescharacteristic
521C2#1307792012yes—
522C2#1307930112yes—
523C2#1307966011yescharacteristic
524C2#1307967111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#540C2
socleC23×C11C22×D4
hypercenterC2×#540D11
hypocenterC11#25611
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10622687C2semidirect
2. C2×#10622681C2semidirect
3. #13074373C2semidirect
4. #13069619C2semidirect
5. #13069612C2semidirect
6. #13069586C2semidirect
7. #13069423C2semidirect
8. #13068964C2semidirect
9. #13068950C2semidirect
10. #13068382C2semidirect
11. C2×C11×#540C2semidirect
52. C11×#127D4semidirect
54. C11×#125D4semidirect
167. C2×#540D11semidirect
314. #127C22⋊D11semidirect
316. #125C22⋊D11semidirect
428. C11#25611semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106226872
C2×#106226812
#130743732
#130696192
#130696122
#130695862
#130694232
#130689642
#130689502
#130683822
C2×C11×#5402
#2561111